Solve for $x$ : $4x^2 + 4x - 360 = 0$
Dividing both sides by $4$ gives: $ x^2 + {1}x {-90} = 0 $ The coefficient on the $x$ term is $1$ and the constant term is $-90$ , so we need to find two numbers that add up to $1$ and multiply to $-90$ The two numbers $10$ and $-9$ satisfy both conditions: $ {10} + {-9} = {1} $ $ {10} \times {-9} = {-90} $ $(x + {10}) (x {-9}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 10) (x -9) = 0$ $x + 10 = 0$ or $x - 9 = 0$ Thus, $x = -10$ and $x = 9$ are the solutions.